‘I’ before ‘E’: Lewis, Language and Languages

Last week, I located Chomsky’s I-language/E-language distinction in the context of Church’s distinction between intensions (procedures) and extensions (sets of ordered pairs). In passing, I mentioned three claims from “Language and Languages” that deserve more attention.

(1) “…a language does not uniquely determine the grammar that generates it.”

(2)  “I know of no promising way to make objective sense of the assertion that

         a grammar Γ is used by a population P, whereas another grammar Γ',

         which generates the same language as Γ, is not.”

(3)  “I think it makes sense to say that languages might be used by populations

        even if there were no internally represented grammars.”

Lewis, who I greatly admire, begins his paper in a way that might seem uncontroversial.

What is a language? Something which assigns meanings to certain strings of types of sounds or of marks. It could therefore be a function, a set of ordered pairs of strings and meanings.

But let’s controvert. Why think that in acquiring a spoken language, one acquires something that assigns meanings to strings? Couldn’t one acquire—i.e., come to implement—a procedure that generates meaningful and pronounceable expressions without assigning anything to anything? (Can’t a machine generate coins that depict people and buildings without assigning buildings to people?) One can stipulate that I-languages assign meanings to strings. But then at least some “meaning assigners” are procedures rather than functions in extension.

Moreover, even if all languages are meaning assigners in some nontrivial sense, why think that Human Languages—languages that human children naturally acquire—could be sets of ordered pairs? There is a thin sense of ‘could’ in which the object beneath my fingers could be a badger (cleverly disguised by an evil demon) rather than a computer. Perhaps it follows that my computer could be a badger. But such thin modal claims don’t help much if you want to know what a computer is. So maybe Lewis' modal claim just indicates the hypothesis that Human Languages are sets of a certain sort. Note, however, that the alleged sets would be quirky.

Recalling an earlier post, (4) is at least roughly synonymous with (5), but not with (6).

           (4)   Was the guest who fed waffles fed the parking meter?

           (5)   The guest who fed waffles was fed the parking meter?

           (6)   The guest who was fed waffles fed the parking meter?

Let <S4, M4> be the string-meaning pair corresponding to (4), and likewise for (5-6). Then on Lewis’ view, the elements of English include <S4, M5> but not <S4, M6>. But why is English not a slightly different set that also includes <S4, M6>? One can stipulate that English is the set it is. But then the question is why humans acquire sets like English as opposed to more inclusive sets. And the answer will be that human children naturally acquire certain generative procedures that allow for homophony only in constrained ways. Similar remarks apply, famously, to ‘easy to please’ and ‘eager to please’. Moreover, if English is a set, does it include <S7, M8> or not?

                        (7)  The child seems sleeping.

                        (8)  The child seems to be sleeping.

Such examples suggest that sets of string-meaning pairs are at best derivative, and that the explanatory action lies with generative procedures; see Aspects of the Theory of Syntax. But one can hypothesize that English is a set that may be specified by a grammar Γ, a distinct grammar Γ', and various procedures that kids implement. So perhaps (1) just makes it explicit that Lewis used ‘language’ in a technical/extensional sense, and in (1), ‘the’ should be ‘any'.

Still, (2) and (3) remain puzzling. If there really are Lewis Languages, why is it so hard to make sense of the idea that speakers specify them in certain ways, and easier to make sense of speakers using Lewis Languages without specifying them procedurally? Did Lewis think that it is senseless to say that a certain machine employs procedure (9) as opposed to (10),

              (9)  F(x) = | x - 1 |

            (10)  F(x) = ⁺√(x² - 2x + 1)

or that it is easier to make sense of the corresponding set being “used by a population” without being specified in any way? I doubt it. While talk of meaning can bring out residual behaviorism and/or verificationism (see Quine, or Kripke’s 1982 book on rule-following), I think it’s more important to highlight Lewis’ slide from talk of meaning to talk of truth and semantics.

What could a meaning of a sentence be? Something which, when combined with factual information about the world...yields a truth value. It could therefore be a function from worlds to truth-values—or more simply, a set of worlds.”

But why not: sentence meanings could be mental representations of a certain sort? If you think Human Language sentences are true or false, relative to contexts, it’s surely relevant that mental representations are (unlike sets) good candidates for being true or false relative to contexts.

Lewis was, of course, exploring a version of the Davidson-Montague Conjecture (DMC) that each Human Language has a classical semantics. As a first pass, let’s say that a language has a classical semantics just in case its expressions are related to entities—e.g., numbers, things covered by good theoretical generalizations, functions and/or mereological sums defined in terms of such things—in a way that can be recursively specified in terms of truth, reference/denotation, or Tarski-style satisfaction conditions. DMC raises many questions about specific constructions. But it also raises the “meta-question” of how a natural language could ever have a semantics.

One possible answer is that Human Languages connect pronunciations with generable representations of suitable entities. But this I-language perspective raises the question of what work the entities do in theories of meaning. And one needn’t be a behaviorist to wonder if ordinary speakers generate the representations required by theories of truth. Lewis held that a Human Language has its semantics by virtue of being used in accord with conventions of truth and trustfulness, “sustained by an interest in communication;” where typically, these conventions are not represented by ordinary speakers. Given extensionally equivalent clusters of conventions, there may be no fact of the matter about which one governs the relevant linguistic behavior. So Lewis was led to an extensional conception of Human Languages. He could offer convention-based accounts of both languages and language (i.e., linguistic behavior). But one can play on the count/mass polysemy differently, and say that language is the use of an I-language. So instead of embracing (2) and (3) as consequences of Lewis’ metasemantics, one might view them as reductios of his extensional conventionalism; see Chomsky, Reflections on Language.

Lewis recognized the possibility of taking Human Languages to be what he called grammars. But he quickly converted this alternative proposal into a methodological question: “Why not begin by saying what it is for a grammar Γ to be used by a population P?” For which, he had an answer: strings are paired with sets of worlds via conventions that do not plausibly determine a unique grammar; better to start by saying what it is for a Lewis Language to be used by a population. But why begin by saying what it is for anything to be used by anyone? Why not start by saying that Human Languages are procedures, partly described by linguists’ grammars, that generate pronounceable meaningful expressions. What might a sentence meaning be? Something which, when it interfaces with human conceptual systems, yields (modulo complications) a truth-evaluable thought. It could therefore be an instruction to build a thought.